\chapter{Experimental Protocols}
\label{chap:experiments}

\section{Hypotheses and Mapping}

We connect theoretical claims to empirical tests via a hypothesis catalogue. Representative entries appear in \cref{tab:hypothesis_catalogue}.

\begin{table}[H]
    \centering
    \caption{Sample hypothesis catalogue}
    \label{tab:hypothesis_catalogue}
    \begin{tabular}{p{4cm}p{4cm}p{4cm}}
        \toprule
        Claim & Experimental observable & Linked chapters \\
        \midrule
        Hierarchical critical surface exists & Peak susceptibility and Binder cumulant crossovers & Ch.~\ref{chap:stat_mech}, Ch.~\ref{chap:simulation} \\
        Controlled noise improves adaptation & Performance vs. noise intensity curve with interior maximum & Ch.~\ref{chap:stochastic} \\
        Macro-level options enhance reward & Policy value improvement under option upgrades & Ch.~\ref{chap:math_framework}, Ch.~\ref{chap:multiagent} \\
        Information bottlenecks align with efficient compression & Mutual information drop at constrained channels & Ch.~\ref{chap:information_theory} \\
        \bottomrule
    \end{tabular}
\end{table}

\section{Experimental Design Patterns}

We employ factorial designs, randomized controlled trials, and ablation studies:
\begin{itemize}
    \item \textbf{Factorial design}: Vary $(J, K, \sigma)$ combinations to map response surfaces.
    \item \textbf{Randomized trials}: Assign governance policies to simulation cohorts to estimate causal effects.
    \item \textbf{Ablations}: Remove specific mechanisms (e.g., top-down control) to measure impact on metrics.
\end{itemize}

Design scripts auto-generate parameter grids and manage replication counts (typically $\geq 30$ per cell for statistical power).

\section{Statistical Analysis Pipelines}

Analysis notebooks compute:
\begin{itemize}
    \item \textbf{Hypothesis tests}: $t$-tests, ANOVA, non-parametric alternatives.
    \item \textbf{Bootstrapping}: Confidence intervals for metrics without closed-form variance.
    \item \textbf{Finite-size scaling}: Collapse curves by rescaling axes, verifying universality.
    \item \textbf{Sensitivity analysis}: Sobol indices and partial rank correlations quantifying parameter influence.
\end{itemize}

Appendix~\ref{app:stat_methods} provides explicit formulas, estimators, and code listings.

\section{Verification and Validation}

\textbf{Verification} confirms the simulation implements intended rules:
\begin{itemize}
    \item Cross-check rule execution logs against theoretical expectations.
    \item Validate instrumentation by injecting known signals and confirming metric detection.
\end{itemize}

\textbf{Validation} assesses fidelity against empirical or analytic references:
\begin{itemize}
    \item Compare aggregated behavior to mean-field predictions or known equilibria.
    \item When domain data are available (Chapter~\ref{chap:case_studies}), align distributional characteristics.
\end{itemize}

\section{Reporting Templates}

Standardized experiment reports include:
\begin{enumerate}
    \item \textbf{Executive summary}: Hypothesis, key findings, implications.
    \item \textbf{Methodology}: Configuration IDs, sample sizes, metrics computed.
    \item \textbf{Results}: Tables and figures with statistical significance annotations.
    \item \textbf{Reproducibility appendix}: Links to raw data, scripts, random seeds, and software versions.
\end{enumerate}

Templates reside under `docs/templates/` and integrate with the changelog process described in Chapter~\ref{chap:introduction}.

